Scale without conformal symmetry in hydrodynamics

Abstract

Keywords

• conformal invariance
• hydrodynamics
• energy-momentum tensor trace
• energy dissipation
• spontaneous symmetry breaking
• hydrodynamic modes

CCDS Authors

Jewel Kumar Ghosh, PhD

Jewel Kumar Ghosh, PhD

• Director, ComPAs Wing

• 

  Assistant Professor

  Department of Physical Sciences

  Independent University, Bangladesh (IUB)

Published at

JHEP, SciPost Physics

References

1. 1.Philippe Di Francesco, Pierre Mathieu, David Sénéchal. (1997). Conformal Field Theory. Graduate texts in contemporary physics[10.1007/978-1-4612-2256-9]
2. 2.Carl Eckart. (1940). The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid. Physical Review, 58(10), 919–924[10.1103/physrev.58.919]
3. 3.Wit Busza, Krishna Rajagopal, Wilke van der Schee. (2018). Heavy Ion Collisions: The Big Picture and the Big Questions. Annual Review of Nuclear and Particle Science, 68(1), 339–376[10.1146/annurev-nucl-101917-020852]
4. 4.Rudolf Baier, Paul Romatschke, Dam Thanh Son, Andrei O Starinets, Mikhail A Stephanov. (2008). Relativistic viscous hydrodynamics, conformal invariance, and holography. Journal of High Energy Physics, 2008(04), 100[10.1088/1126-6708/2008/04/100]
5. 5.Zohar Komargodski, Adam Schwimmer. (2011). On renormalization group flows in four dimensions. Journal of High Energy Physics, 2011(12)[10.1007/jhep12(2011)099]
6. 6.Dam T. Son, Andrei O. Starinets. (2007). Viscosity, Black Holes, and Quantum Field Theory. Annual Review of Nuclear and Particle Science, 57(1), 95–118[10.1146/annurev.nucl.57.090506.123120]
7. 7.Pavel Kovtun. (2012). Lectures on hydrodynamic fluctuations in relativistic theories. Journal of Physics A Mathematical and Theoretical, 45(47), 473001[10.1088/1751-8113/45/47/473001]
8. 8.Joseph Polchinski. (1988). Scale and conformal invariance in quantum field theory. Nuclear Physics B, 303(2), 226–236[10.1016/0550-3213(88)90179-4]
9. 9.Paul Romatschke, Ulrike Romatschke. (2019). Relativistic Fluid Dynamics in and out of Equilibrium. Cambridge University Press eBooks[10.1017/9781108651998]
10. 10.Kristan Jensen, Matthias Kaminski, Pavel Kovtun, René Meyer, Adam Ritz, Amos Yarom. (2012). Towards Hydrodynamics without an Entropy Current. Physical Review Letters, 109(10), 101601[10.1103/physrevlett.109.101601]
11. 11.Pavel Kovtun. (2019). First-order relativistic hydrodynamics is stable. Journal of High Energy Physics, 2019(10)[10.1007/jhep10(2019)034]
12. 12.C. P. Herzog, P. K. Kovtun, D. T. Son. (2009). Holographic model of superfluidity. Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields, 79(6)[10.1103/physrevd.79.066002]
13. 13.Yu Nakayama. (2014). Scale invariance vs conformal invariance. Physics Reports, 569, 1–93[10.1016/j.physrep.2014.12.003]
14. 14.J. Wess. (1960). The conformal invariance in quantum field theory. Il Nuovo Cimento, 18(6), 1086–1107[10.1007/bf02733168]
15. 15.Steven S. Gubser, Amos Yarom. (2011). Conformal hydrodynamics in Minkowski and de Sitter spacetimes. Nuclear Physics B, 846(3), 469–511[10.1016/j.nuclphysb.2011.01.012]
16. 16.R Loganayagam. (2008). Entropy current in conformal hydrodynamics. Journal of High Energy Physics, 2008(05), 087[10.1088/1126-6708/2008/05/087]
17. 17.Sayantani Bhattacharyya, R Loganayagam, Ipsita Mandal, Shiraz Minwalla, Ankit Sharma. (2008). Conformal nonlinear fluid dynamics from gravity in arbitrary dimensions. Journal of High Energy Physics, 2008(12), 116[10.1088/1126-6708/2008/12/116]
18. 18.Sheer El-Showk, Yu Nakayama, Slava Rychkov. (2011). What Maxwell theory in d ≠ 4 teaches us about scale and conformal invariance. Nuclear Physics B, 848(3), 578–593[10.1016/j.nuclphysb.2011.03.008]
19. 19.Kristan Jensen. (2018). On the coupling of Galilean-invariant field theories to curved spacetime. SciPost Physics, 5(1)[10.21468/scipostphys.5.1.011]
20. 20.Jan de Boer, Jelle Hartong, Niels Obers, Watse Sybesma, Stefan Vandoren. (2018). Perfect fluids. SciPost Physics, 5(1)[10.21468/scipostphys.5.1.003]
21. 21.Anatoly Dymarsky, Zohar Komargodski, Adam Schwimmer, Stefan Theisen. (2015). On scale and conformal invariance in four dimensions. Journal of High Energy Physics, 2015(10)[10.1007/jhep10(2015)171]
22. 22.Francesco Coradeschi, Paolo Lodone, Duccio Pappadopulo, Riccardo Rattazzi, Lorenzo Vitale. (2013). A naturally light dilaton. Journal of High Energy Physics, 2013(11)[10.1007/jhep11(2013)057]
23. 23.A. Iorio, L. O'Raifeartaigh, I. Sachs, C. Wiesendanger. (1997). Weyl gauging and conformal invariance. Nuclear Physics B, 495(1-2), 433–450[10.1016/s0550-3213(97)00190-9]
24. 24.V. Riva, J. Cardy. (2005). Scale and conformal invariance in field theory: a physical counterexample. Physics Letters B, 622(3-4), 339–342[10.1016/j.physletb.2005.07.010]
25. 25.Sayantani Bhattacharyya. (2014). Entropy current and equilibrium partition function in fluid dynamics. Journal of High Energy Physics, 2014(8)[10.1007/jhep08(2014)165]
26. 26.Jan de Boer, Jelle Hartong, Niels Obers, Watse Sybesma, Stefan Vandoren. (2018). Hydrodynamic modes of homogeneous and isotropic fluids. SciPost Physics, 5(2)[10.21468/scipostphys.5.2.014]
27. 27.Georgios Papadopoulos, Edward Witten. (2025). Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry. Journal of High Energy Physics, 2025(3)[10.1007/jhep03(2025)056]
28. 28.Georgios Itsios, Konstantinos Sfetsos, Konstantinos Siampos. (2021). Kerr–Schild perturbations of coset CFTs as scale invariant integrable σ-models. Nuclear Physics B, 973, 115594[10.1016/j.nuclphysb.2021.115594]
29. 29.R Jackiw, S-Y Pi. (2011). Tutorial on scale and conformal symmetries in diverse dimensions. Journal of Physics A Mathematical and Theoretical, 44(22), 223001[10.1088/1751-8113/44/22/223001]
30. 30.Yu Nakayama. (2012). Higher derivative corrections in holographic Zamolodchikov–Polchinski theorem. The European Physical Journal C, 72(2)[10.1140/epjc/s10052-012-1870-z]
31. 31.Ali Naseh. (2016). Scale versus conformal invariance from entanglement entropy. Physical review. D/Physical review. D., 94(12)[10.1103/physrevd.94.125015]
32. 32.Omar Zanusso. (2023). Consequences of gauging the Weyl symmetry and the two-dimensional conformal anomaly. Physical review. D/Physical review. D., 108(12)[10.1103/physrevd.108.125018]
33. 33.Riccardo Argurio, Carlos Hoyos, Daniele Musso, Daniel Naegels. (2020). Gapped dilatons in scale invariant superfluids. Physical review. D/Physical review. D., 102(7)[10.1103/physrevd.102.076011]
34. 34.Victor Lekeu. (2021). Modave lecture notes: two useful topics in Lie algebras. , 001[10.22323/1.389.0001]
35. 35.Rudolf Baier, Fakultät Für Physik, Paul Romatschke, Dam Thanh Son, Andrei O. Starinets, Mikhail A. Stephanov. (2008). Relativistic viscous hydrodynamics, conformal invariance, and holography.
36. 36.Sayantani Bhattacharyya A, R. Loganayagam A, Ipsita M, Al B, Shiraz Minwalla A, Ankit Sharma C, Homi Bhabha Rd. (2013). Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions.
37. 37.Jackiw, Roman, Pi, So-Young. (2011). Tutorial on scale and conformal symmetries in diverse dimensions. DSpace@MIT (Massachusetts Institute of Technology)[link]

Cited By

1. 1.Jewel Kumar Ghosh, Francisco Peña-Benítez, Patricio Salgado-Rebolledo. (2025). Hydrostatic equilibrium in multi-Weyl semimetals. Journal of High Energy Physics, 2025(10)[10.1007/jhep10(2025)055]